Consider a particle in a 1D half-infinite well. The potential in region III is infinite and is zero in region I. In this case however, the potential is not infinite in region II but has a constant value Vo. V(A)-{ 00 0 x L III 20 I X-L II Region III a. Write the Schrodinger equation in region III. What is the only acceptable solution? Region I b. Write the Schrodinger equation in region I. Show that , Asin(kx) + Bcos (kx) is solution of this equation and give the constant kas a function of the total energy E of the particle. c. Using continuity of the wave function at the boundary between region III and I, determine the constant B. Region II -ix d. Write the Schrodinger equation in region II. Show that ,,Ce + De is solution of this equation and give the constant as a function of the total energy E